arXiv subjects

Goran Strbac

Publications and source records attributed to Goran Strbac.

At least 37 records · Page 2Linked to original sources

arXiv2022

A framework for receding-horizon control in infinite-horizon aggregative games

A novel modelling framework is proposed for the analysis of aggregative games on an infinite-time horizon, assuming that players are subject to heterogeneous periodic constraints. A new aggregative equilibrium notion is presented and the strategic behaviour of the agents is analysed under a receding horizon paradigm. The evolution of the strategies predicted and implemented by the players over time is modelled through a discrete-time multi-valued dynamical system. By considering Lyapunov stability notions and applying limit and invariance results for set-valued correspondences, necessary conditions are derived for convergence of a receding horizon map to a periodic equilibrium of the aggregative game. This result is achieved for any (feasible) initial condition, thus ensuring implicit adaptivity of the proposed control framework to real-time variations in the number and parameters of players. Design and implementation of the proposed control strategy are discussed and an example of distributed control for data routing is presented, evaluating its performance in simulation.

eess.SY↗

arXiv2022

Multi-model assessment of heat decarbonisation options in the UK using electricity and hydrogen

Delivering low-carbon heat will require the substitution of natural gas with low-carbon alternatives such as electricity and hydrogen. The objective of this paper is to develop a method to soft-link two advanced, investment-optimising energy system models, RTN (Resource-Technology Network) and WeSIM (Whole-electricity System Investment Model), in order to assess cost-efficient heat decarbonisation pathways for the UK while utilising the respective strengths of the two models. The linking procedure included passing on hourly electricity prices from WeSIM as input to RTN, and returning capacities and locations of hydrogen generation and shares of electricity and hydrogen in heat supply from RTN to WeSIM. The outputs demonstrate that soft-linking can improve the quality of the solution, while providing useful insights into the cost-efficient pathways for zero-carbon heating. Quantitative results point to the cost-effectiveness of using a mix of electricity and hydrogen technologies for delivering zero-carbon heat, also demonstrating a high level of interaction between electricity and hydrogen infrastructure in a zero-carbon system. Hydrogen from gas reforming with carbon capture and storage can play a significant role in the medium term, while remaining a cost-efficient option for supplying peak heat demand in the longer term, with the bulk of heat demand being supplied by electric heat pumps.

eess.SY↗

arXiv2022

Value of Optimal Trip and Charging Scheduling of Commercial Electric Vehicle Fleets with Vehicle-to-Grid in Future Low Inertia Systems

The electrification of transport is seen as an important step in the global decarbonisation agenda. With such a large expected load on the power system from electric vehicles (EVs), it is important to coordinate charging in order to balance the supply and demand for electricity. Bidirectional charging, enabled through Vehicle-to-Grid (V2G) technology, will unlock significant storage capacity from stationary EVs that are plugged in. To take this concept a step further, this paper quantifies the potential revenues to be gained by a commercial EV fleet operator from simultaneously scheduling its trips on a day-ahead basis, as well as its charging. This allows the fleet to complete its trips (with user defined trip length and distance), while taking advantage of fluctuating energy and ancillary services prices. A mathematical framework for optimal trip scheduling is proposed, formulated as a mixed-integer linear program, and is applied to several relevant scenarios of the present and future British electricity system. It is demonstrated that an optimal journey start time can increase the revenue of commercial fleets by up to 38% in summer and 12% in winter. This means a single EV from the maintenance fleet can make additional annual revenue of up to £729. Flexible trip schedules are more valuable in the summer because keeping EVs plugged in during peak solar output will benefit the grid and the fleet operators the most. It was also found that a fleet of 5,000 EVs would result in the equivalent $\textrm{CO}_2$ of removing one Combined Cycle Gas Turbine from the system. This significant increase in revenue and carbon savings show this approach is worth investigating for potential future application.

eess.SY↗

arXiv2022

Values of Coordinated Residential Space Heating in Demand Response Provision

Demand-side response from space heating in residential buildings can potentially provide a huge amount of flexibility for the power system, particularly with deep electrification of the heat sector. In this context, this paper presents a novel distributed control strategy to coordinate space heating across numerous residential households with diversified thermal parameters. By employing an iterative algorithm under the game-theoretical framework, each household adjusts its own heating schedule through demand shift and thermal comfort compensation with the purpose of achieving individual cost savings, whereas the aggregate peak demand is effectively shaved on the system level. Additionally, an innovative thermal comfort model which considers both the temporal and spatial differences in customised thermal comfort requirements is proposed. Through a series of case studies, it is demonstrated that the proposed space heating coordination strategy can facilitate effective energy arbitrage for individual buildings, driving a 13.96% reduction in system operational cost and 28.22% peak shaving. Moreover, the superiority of the proposed approach in thermal comfort maintenance is numerically analysed based on the proposed thermal comfort quantification model.

eess.SY↗

arXiv2022

On optimal coordinated dispatch for heterogeneous storage fleets with partial availability

This paper addresses the problem of optimal scheduling of an aggregated power profile (during a coordinated discharging or charging operation) by means of a heterogeneous fleet of storage devices subject to availability constraints. Devices have heterogeneous initial levels of energy, power ratings and efficiency; moreover, the fleet operates without cross-charging of the units. An explicit feedback policy is proposed to compute a feasible schedule whenever one exists and scalable design procedures to achieve maximum time to failure or minimal unserved energy in the case of unfeasible aggregated demand profiles. Finally, a time-domain characterization of the set of feasible demand profiles using aggregate constraints is proposed, suitable for optimization problems where the aggregate population behaviour is of interest.

math.OC↗

arXiv2022

Value of Fleet Vehicle Grid in Providing Transmission System Operator Services

In this paper a new aggregated model for electric vehicle (EV) fleets is presented that considers their daily and weekly usage patterns. A frequency-constrained stochastic unit commitment model is employed to optimally schedule EV charging and discharging as well as the provision of frequency response (FR) in an electricity system, while respecting the vehicles' energy requirements and driving schedules. Through case studies we demonstrate that an EV with vehicle to grid (V2G) capability can reduce system costs in a future GB electricity grid by up to £12,000 per year, and reduce CO2 emissions by 60 tonnes per year, mainly due to reduced curtailment of wind power. The paper also quantifies the changes in the benefits of fleet V2G resulting from variations in FR delivery time, the penetration of wind or uptake of alternative flexibility providers. Finally , a battery degradation model dependent on an EV's state of charge is proposed and implemented in the stochastic scheduling problem. It enables significant degradation cost reductions of 16% with only a 0.4% reduction of an EV's system value.

eess.SY↗

arXiv2021

Probabilistic Scheduling of UFLS to Secure Credible Contingencies in Low Inertia Systems

The reduced inertia levels in low-carbon power grids necessitate explicit constraints to limit frequency's nadir and rate of change during scheduling. This can result in significant curtailment of renewable energy due to the minimum generation of thermal plants that are needed to provide frequency response (FR) and inertia. Additional consideration of fast FR, a dynamically reduced largest loss and under frequency load shedding (UFLS) allows frequency security to be achieved more cost effectively. This paper derives a novel nadir constraint from the swing equation that, for the first time, provides a framework for the optimal comparison of all these services. We demonstrate that this constraint can be accurately and conservatively approximated for moderate UFLS levels with a second order cone, resulting in highly tractable convex problems. Case studies performed on a Great Britain 2030 system demonstrate that UFLS as an option to contain single plant outages can reduce annual operational costs by up to £559m, 52% of frequency security costs. The sensitivity of this value to wind penetration, abundance of alternative frequency services, UFLS amount and cost is explored.

eess.SY↗

arXiv2021

Exact aggregate models for optimal management of heterogeneous fleets of storage devices

Future power grids will entail large fleets of storage devices capable of scheduling their charging/discharging profiles so as to achieve lower peak demand and reduce energy bills, by shifting absorption times in sync with the availability of renewable energy sources. Optimal management of such fleets entails large scale optimisation problems which are better dealt with in a hierarchical manner, by clustering together individual devices into fleets. Leveraging on recent results characterizing the set of aggregate demand profiles of a heterogeneous fleet of charging (or, respectively, discharging) devices we propose a way to achieve optimality, in a unit commitment problem, by adopting a simplified formulation with a number of constraints for the fleet that scales linearly in the number of time-slots considered and is independent of the size of the fleet. This is remarkable, as it shows that, under suitable conditions, a heterogeneous fleet of any size can effectively be treated as a single storage unit.

math.OC↗

arXiv2021

Conditions for Regional Frequency Stability in Power System Scheduling -- Part II: Application to Unit Commitment

In Part I of this paper we have introduced the closed-form conditions for guaranteeing regional frequency stability in a power system. Here we propose a methodology to represent these conditions in the form of linear constraints and demonstrate their applicability by implementing them in a generation-scheduling model. This model simultaneously optimises energy production and ancillary services for maintaining frequency stability in the event of a generation outage, by solving a frequency-secured Stochastic Unit Commitment (SUC). We consider the Great Britain system, characterised by two regions that create a non-uniform distribution of inertia: England in the South, where most of the load is located, and Scotland in the North, containing significant wind resources. Through several case studies, it is shown that inertia and frequency response cannot be considered as system-wide magnitudes in power systems that exhibit inter-area oscillations in frequency, as their location in a particular region is key to guarantee stability. In addition, securing against a medium-sized loss in the low-inertia region proves to cause significant wind curtailment, which could be alleviated through reinforced transmission corridors. In this context, the proposed constraints allow to find the optimal volume of ancillary services to be procured in each region.

math.OC↗

arXiv2021

Conditions for Regional Frequency Stability in Power System Scheduling -- Part I: Theory

This paper considers the phenomenon of distinct regional frequencies recently observed in some power systems. First, a reduced-order mathematical model describing this behaviour is developed. Then, techniques to solve the model are discussed, demonstrating that the post-fault frequency evolution in any given region is equal to the frequency evolution of the Centre Of Inertia plus certain inter-area oscillations. This finding leads to the deduction of conditions for guaranteeing frequency stability in all regions of a power system, a deduction performed using a mixed analytical-numerical approach that combines mathematical analysis with regression methods on simulation samples. The proposed stability conditions are linear inequalities that can be implemented in any optimisation routine allowing the co-optimisation of all existing ancillary services for frequency support: inertia, multi-speed frequency response, load damping and an optimised largest power infeed. This is the first reported mathematical framework with explicit conditions to maintain frequency stability in a power system exhibiting inter-area oscillations in frequency.

math.OC↗

arXiv2021

Importance of Linking Inertia and Frequency Response Procurement: The Great Britain Case

In order to decarbonise the electricity sector, the future Great Britain (GB) power system will be largely dominated by non-synchronous renewables. This will cause low levels of inertia, a key parameter that could lead to frequency deterioration. Therefore, the requirement for ancillary services that contain frequency deviations will increase significantly, particularly given the increase in size of the largest possible loss with the commissioning of large nuclear plants in the near future. In this paper, an inertia-dependent Stochastic Unit Commitment (SUC) model is used to illustrate the benefits of linking inertia and frequency response provision in low-inertia systems. We demonstrate that the cost of procuring ancillary services in GB could increase by 165% if the level of inertia is not explicitly considered when procuring frequency response. These results highlight the need to re-think the structure of ancillary-services markets, which in GB are nowadays held one month ahead of delivery.

math.OC↗

arXiv2021

Ancillary services in Great Britain during the COVID-19 lockdown: a glimpse of the carbon-free future

The COVID-19 pandemic led to partial or total lockdowns in several countries during the first half of 2020, which in turn caused a depressed electricity demand. In Great Britain (GB), this low demand combined with large renewable output at times, created conditions that were not expected until renewable capacity increases to meet emissions targets in coming years. The GB system experienced periods of very high instantaneous penetration of non-synchronous renewables, compromising system stability due to the lack of inertia in the grid. In this paper, a detailed analysis of the consequences of the lockdown on the GB electricity system is provided, focusing on the ancillary services procured to guarantee stability. Ancillary-services costs increased by £200m in the months of May to July 2020 compared to the same period in 2019 (a threefold increase), highlighting the importance of ancillary services in low-carbon systems. Furthermore, a frequency-secured scheduling model is used in the present paper to showcase the future trends that GB is expected to experience, as penetration of renewables increases on the road to net-zero emissions by 2050. Several sensitivities are considered, demonstrating that the share of total operating costs represented by ancillary services could reach 35%.

eess.SY↗

arXiv2020

Low-complexity decentralized algorithm for aggregate load control of thermostatic loads

Thermostatically controlled loads such as refrigerators are exceptionally suitable as a flexible demand resource. This paper derives a decentralised load control algorithm for refrigerators. It is adapted from an existing continuous time control approach, with the aim to achieve low computational complexity and an ability to handle discrete time steps of variable length -- desirable features for embedding in appliances and high-throughput simulations. Simulation results of large populations of heterogeneous appliances illustrate the accurate aggregate control of power consumption and high computational efficiency. Tracking accuracy is quantified as a function of population size and time step size, and correlations in the tracking error are investigated. The controller is shown to be robust to errors in model specification and to sudden perturbations in the form of random refrigerator door openings.

eess.SY↗

arXiv2020

A Machine-learning based Probabilistic Perspective on Dynamic Security Assessment

Probabilistic security assessment and real-time dynamic security assessments (DSA) are promising to better handle the risks of system operations. The current methodologies of security assessments may require many time-domain simulations for some stability phenomena that are unpractical in real-time. Supervised machine learning is promising to predict DSA as their predictions are immediately available. Classifiers are offline trained on operating conditions and then used in real-time to identify operating conditions that are insecure. However, the predictions of classifiers can be sometimes wrong and hazardous if an alarm is missed for instance. A probabilistic output of the classifier is explored in more detail and proposed for probabilistic security assessment. An ensemble classifier is trained and calibrated offline by using Platt scaling to provide accurate probability estimates of the output. Imbalances in the training database and a cost-skewness addressing strategy are proposed for considering that missed alarms are significantly worse than false alarms. Subsequently, risk-minimised predictions can be made in real-time operation by applying cost-sensitive learning. Through case studies on a real data-set of the French transmission grid and on the IEEE 6 bus system using static security metrics, it is showcased how the proposed approach reduces inaccurate predictions and risks. The sensitivity on the likelihood of contingency is studied as well as on expected outage costs. Finally, the scalability to several contingencies and operating conditions are showcased.

eess.SY↗

arXiv2020

Challenges and opportunities of inertia estimation and forecasting in low-inertia power systems

Accurate inertia estimates and forecasts are crucial to support the system operation in future low-inertia power systems. A large literature on inertia estimation methods is available. This paper aims to provide an overview and classification of inertia estimation methods. The classification considers the time horizon the methods are applicable to, i.e., offline post mortem, online real time and forecasting methods, and the scope of the inertia estimation, e.g., system-wide, regional, generation, demand, individual resource. Shortcomings of the existing inertia estimation methods have been identified and suggestions for future work have been made.

eess.SY↗

arXiv2020

Value of Point-of-load Voltage Control for Enhanced Frequency Response in Future GB Power System

The need for Enhanced Frequency Response (EFR) is expected to increase significantly in future low-carbon Great Britain (GB) power system. One way to provide EFR is to use power electronic compensators (PECs) for point-of-load voltage control (PVC) to exploit the voltage dependence of loads. This paper investigates the techno-economic feasibility of such technology in future GB power system by quantifying the total EFR obtainable through deploying PVC in the urban domestic sector, the investment cost of the installment and the economic and environmental benefits of using PVC. The quantification is based on a stochastic domestic demand model and generic medium and low-voltage distribution networks for the urban areas of GB and a stochastic unit commitment (SUC) model with constraints for secure post-fault frequency evolution is used for the value assessment. Two future energy scenarios in the backdrop of 2030 with `smart' and `non-smart' control of electric vehicles and heat pumps, under different levels of penetration of battery energy storage system (BESS) are considered to assess the value of PEC, as well as the associated payback period. It is demonstrated that PVC could effectively complement BESS towards EFR provision in future GB power system.

eess.SY↗

arXiv2020

Optimal Portfolio of Distinct Frequency-Response Services in Low-Inertia Systems

A reduced level of system inertia due to renewable integration increases the need for cost-effective provision of ancillary services, such as Frequency Response (FR). In this paper we propose a closed-form solution to the differential equation describing frequency dynamics, which allows to obtain frequency-security algebraic constraints to be implemented in optimisation routines. This is done while considering any finite number of FR services with distinguished characteristics, such as different delivery times and activation delays. The problem defined by these frequency-security constraints can be formulated as a Mixed-Integer Second-Order Cone Program (MISOCP), which can be efficiently handled by off-the-shelf conic optimisation solvers. This paper also takes into account the uncertainty in inertia contribution from the demand side by formulating the frequency-security conditions as chance constraints, for which an exact convex reformulation is provided. Finally, case studies highlighting the effectiveness of this frequency-secured formulation are presented.

math.OC↗

arXiv2020

Accelerating System Adequacy Assessment using the Multilevel Monte Carlo Approach

Accurately and efficiently estimating system performance under uncertainty is paramount in power system planning and operation. Monte Carlo simulation is often used for this purpose, but convergence may be slow, especially when detailed models are used. Previously published methods to speed up computations may severely constrain model complexity, limiting their real-world effectiveness. This paper uses the recently proposed Multilevel Monte Carlo (MLMC) framework, which combines outputs from a hierarchy of simulators to boost computational efficiency without sacrificing accuracy. It explains which requirements the MLMC framework imposes on the model hierarchy, and how these naturally occur in power system adequacy assessment problems. Two adequacy assessment examples are studied in detail: a composite system and a system with heterogeneous storage units. An intuitive speed metric is introduced for easy comparison of simulation setups. Depending on the problem and metric of interest, large speedups can be obtained.

stat.CO↗